There have been various geometry based approaches to characterize and quantify entanglement [1]}, [2]}, [3]}, [4]}, [5]}. Recently, a geometric perspective of I-concurrence has been given for multiparty entangled system of qudits, based on wedge product [6]} and Lagrange's identity, a generalisation of the Brahmagupta–Fibonacci identity [7]}. This framework was further explored in [5]}, where geometric representation of three way distributive entanglement, known as 3-tangle [9]} in two dimensions is given, with a measure to quantify the distributive \(n\) -\(\text{party}\)  entanglement. In [3]}, the minimum distance between a set of bi-partite n qudit density matrices with positive partial trace and maximally mixed states was calculated using a measure based on Euclidean distance between Hermitian matrices. Here, we use this wedge product formalism [4]} to find geometrical configurations corresponding to the separable and maximally entangled states of finite dimensional multiparty systems. The concurrence corresponding to the bi-partitions of the multiparty system is expressed in terms of the wedge product of the post measurement vectors. Parallelism of post measurement vectors result in separability across the bi-partitions, whereas the orthogonality and equality of these vectors yield maximally entangled states. These constraints are employed to find maximally entangled states in case of two qubit and three qubit systems. For the two qubit case, one obtains the general expression of the maximally entangled states, which after local unitary transformations lead to the Bell states. In the three qubit case, starting with the Schmidt decomposed canonical forms [12]}, [13]}, we naturally obtain GHZ and GHZ like states [14]}, as maximally entangled states. We then characterize and compare these states with the W-state using the polynomial invariant 3-tangle [9]}, defined in the wedge product formalism [5]}. The general conditions for maximally entangled states of a two qudit system is established leading to the generalised Bell states. We further describe a procedure to construct density matrices in terms of inner product of post measurement vectors. In addition to being efficient, this approach provides insight to the geometric origin of absolute maximal entanglement [17]} and intrinsic coherence [18]}. The intrinsic degree of coherence is written in terms of post-measurement vectors and shown that, the geometric conditions for extremum of intrinsic coherence are opposite to those of the entanglement.
